SOLUTION: Jim started with an empty piggy bank.Each day, he put a penny, a dime and a quarter into his piggy bank. He kept this up until the bank contained and exact number of dollars, not s

Question 1092998: Jim started with an empty piggy bank.Each day, he put a penny, a dime and a quarter into his piggy bank. He kept this up until the bank contained and exact number of dollars, not s penny more or less, how many days did this take, and how many dollars did the bank finally contain?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The amount of many Jim put in his Piggy bank each day, in cents, is

After days, with being a positive integer,
Jim had cents in his piggy bank,
and that was exactly dollars, with being a positive integer.
Those dollars were exactly cents.
At that point it was true that .
If we factor the numbers we know, we can write that equation as
---> .
As and have no common factors other than ,
and and are positive integers,
must be a multiple of ,
and the first time that could happen it would be after days.
At that point, Jim's piggy bank would have held
.
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